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Bivariate Data Analysis Worksheet

Read paired quantitative data and explain association without claiming causation. Includes a worked example, printable practice, and an answer key with explanations.

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Grade 9 Math Probability and StatisticsBivariate Data

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Includes

2 TextMultiple ChoiceFill in the BlanksShort AnswerCustomTrue / FalseMatchingLong Answer

Standards

CCSS.MATH.CONTENT.HSS.ID.B.5CCSS.MATH.CONTENT.HSS.ID.B.6CCSS.MATH.CONTENT.HSS.ID.C.7

Topics

MathGrade 9Bivariate DataStatisticsScatter PlotsCorrelation
11 sections · Free to use · Printable
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Bivariate Data Analysis

Name:

Date:

Score:

Learning goal and worked example

Read paired quantitative data and explain association without claiming causation.

A point (3,40) means 3 hours of study and a score of 40. A rising pattern suggests positive association; it does not prove extra study caused the score.

Prerequisites: coordinates, graph scales, and variables.

Read each question carefully and answer to the best of your ability. Show all your work when necessary.

1. Which of the following describes bivariate data?

a

Data with a single variable.

b

Data involving two variables.

c

Data with more than two variables.

d

Data that is always categorical.

2. What type of graph is typically used to display two quantitative variables measured on the same individuals?

a

Bar graph

b

Histogram

c

Scatter plot

d

Pie chart

1. When two variables tend to move in the same direction, they have a   correlation.

2. A line of   is used to model the relationship between two variables in a scatter plot.

3. The variable that is being predicted or explained is called the   variable.

1. Describe the difference between positive and negative correlation, providing an example for each.

Illustrative data (hours studied, score out of 100): (1,20), (2,30), (3,40), (4,50), (5,60), (6,70), (7,80), (8,90), (9,95), (10,100). These invented observations demonstrate association, not a controlled experiment.

Study hours and test scores0011022033044055066077088099010100Study hours and test scoresHours studiedScore out of 100

1. Based on the scatter plot, what type of correlation exists between hours studied and test scores?

2. If a student studied for 7 hours, what would you predict their test score to be based on the general trend?

1. A strong correlation always implies causation.

T

True

F

False

2. Outliers can significantly affect the slope of the line of best fit.

T

True

F

False

Match the term on the left with its definition on the right.

1. Correlation Coefficient

 

a. A value that describes the strength and direction of a linear relationship between two variables.

2. Independent Variable

 

b. The variable that is manipulated or changed in an experiment.

3. Dependent Variable

 

c. The variable that is measured or observed and is affected by the independent variable.

1. Explain how to determine if a line of best fit is a good model for a given set of bivariate data.

Answer key and worked solutions

Multiple choice: 1 b (two paired variables); 2 c (scatter plot).

Fill in the blanks: 1 positive; 2 best fit; 3 response (or dependent).

Short answer 1: Positive association means larger values of one variable tend to accompany larger values of the other, such as height and arm span. Negative association means larger values tend to accompany smaller values, such as a vehicle’s age and resale value. These are illustrative tendencies, not universal laws.

Scatter plot: 1 strong positive association; 2 approximately 80 points. The given observation at 7 hours is 80; a trend-based estimate near it is reasonable.

True/false: 1 False—correlation alone does not establish causation. 2 True—an influential outlier can change the fitted slope.

Matching: 1 a; 2 b; 3 c. In observational work, “explanatory” and “response” avoid implying experimental control.

Extended response: A useful linear fit follows the overall trend, with small residuals and no clear curved pattern in residuals. Check outliers and the range of observed x values; a high correlation alone does not justify extrapolation.

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